Suppose there are two classes in a school, one with 20 students and one with 25. If the first class has 10 girls and the second class has 12, which class has more girls? Note 2

Video SegmentIn this video segment, participants share their answers to Problem A1 with Professor Cossey. Watch the segment after completing Problem A1, and compare your answer with those of the onscreen participants. If you get stuck on the problem, you can watch the video segment to help you.

What different definitions of "more" are used here?
What is your definition of "more"?

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If you said that the second class has more girls, you're making an absolute comparison. You probably thought that 12 is 2 more than 10, so there are more girls in the class with 12.

If you said that the first class has more girls, you're making a relative comparison. You probably thought 10 is half of 20, and 12 is less then half of 25, so there are more girls in the class with 10.

Clearly these are two different interpretations of "more." Although both interpretations are correct, in some cases it is more appropriate to look at relative rather than absolute comparisons. For example, compare an all-girl class of 20 students with a class of 25 students, 22 of whom are girls. In a sense, there are "more" girls in the class with 20.

Problem A2

Describe the numerical calculations you would do with two numbers to make an absolute comparison.

Problem A3

Describe the numerical calculations you would do with two numbers to make a relative comparison.

Problem A4

Give some examples of situations where it is more useful to make an absolute comparison. Give some examples of situations where it is more useful to make a relative comparison.

Problem A5

Suppose the average height of eighth grade students is greater than the average height of seventh grade students. Is this an absolute or relative comparison? Why?